Automatic frequency extraction using sinusoidal approximation and wavelet transform

This paper introduces a novel time-frequency-based pattern recognition technique for gear fault identification using time-domain analysis of continuous wavelet transform. It, moreover, presents a new approximation method for gearbox vibration signals. Sinusoidal approximation approximates sinusoidal components of noisy vibration signals generated from gearboxes using autocorrelation of wavelet coefficients. First, the shortcomings of continuous wavelet transform have been ameliorated using autocorrelation function. Then, the autocorrelation of wavelet coefficients have been introduced as an original feature for monitoring purposes of gearbox diagnostics. Finally, a sinusoidal function has been further considered to approximate the periodic waveforms of autocorrelation coefficients for both normal and faulty gearboxes. As reported in this paper, gearbox vibration signals with non-stationary characteristics can be properly classified with minimal loss of information in frequency contents using the sinusoidal approximation of generated autocorrelation waveforms of wavelet coefficients.